Math 2325
Project 5 (Chapter 14) - Iteration of Quadratic Functions

Helmut Knaust, Department of Mathematical Sciences, UTEP, El Paso TX 79968
hknaust@utep.edu
10/31/2012.Last edit 03/28/2017.

The graph of f(x)=a x (1-x) for values of a between 2 and 4:

Manipulate[(f[x_]:=a x (1-x);Plot[{f[x],x},{x,0,1},ImageSize->600,PlotStyle->{{Red,Thick},{Dashed}}]),{a,2,4,.1}]

The additional blue graph shows the composition of the function f with itself :

Manipulate[(f[x_]:=a x (1-x);Plot[{f[x],f[f[x]],x},{x,0,1},ImageSize->600,PlotStyle->{{Red,Thick},{Blue,Thick},{Dashed}}]),{a,2,4,.1}]

The additional green graph shows the 4-fold composition of the function f with itself.

Manipulate[(f[x_]:=a x (1-x);Plot[{f[x],f[f[x]],f[f[f[f[x]]]],x},{x,0,1},ImageSize->600,PlotStyle->{{Red,Thick},{Blue,Thick},{Green,Thick},{Dashed}}]),{a,2,4,.1}]